Related papers: Computation of conformal invariants
Current instance segmentation models achieve high performance on average predictions, but lack principled uncertainty quantification: their outputs are not calibrated, and there is no guarantee that a predicted mask is close to the ground…
We describe an efficient algorithm to compute a conformally equivalent metric for a discrete surface, possibly with boundary, exhibiting prescribed Gaussian curvature at all interior vertices and prescribed geodesic curvature along the…
We discuss solutions of several questions concerning the geometry of conformal planes.
In this paper we give a general family of conformal invariants associated to bordered Riemann surfaces endowed with boundary parametrizations, or equivalently compact surfaces endowed with conformal maps. Each invariant is specified by a…
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…
Here we construct the conformal mappings with the help of continuous fractions approximations. These approximations converge to the algebraic roots $\sqrt[N]{z}$ for $N \in \mathbb{N}$ and $z$ from the right half-plane of the complex plane.…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
We describe algorithms for computing geometric invariants for Hilbert modular surfaces, and we report on their implementation.
We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
In many applications, the information about the number of eigenvalues inside a given region is required. In this paper, we propose a contour-integral based method for this purpose. The new method is motivated by two findings. There exist…
We compute the measure with multiplicity of the set of complex planes intersecting a compact domain in a complex space form. The result is given in terms of the so-called hermitian intrinsic volumes. Moreover, we obtain two different…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which…
We consider overdetermined problems related to the fractional capacity. In particular we study $s$-harmonic functions defined in unbounded exterior sets or in bounded annular sets, and having a level set parallel to the boundary. We first…
The invariant theory for conformal hypersurfaces is studied by treating these as the conformal infinity of a conformally compact manifold: For a given conformal hypersurface embedding, a distinguished ambient metric is found (within its…